Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x - 6} = \dfrac{36}{x - 6}$
Solution: Multiply both sides by $x - 6$ $ \dfrac{x^2}{x - 6} (x - 6) = \dfrac{36}{x - 6} (x - 6)$ $ x^2 = 36$ Subtract $36$ from both sides: $ x^2 - (36) = 36 - (36)$ $ x^2 - 36 = 0$ Factor the expression: $ (x + 6)(x - 6) = 0$ Therefore $x = -6$ or $x = 6$ However, the original expression is undefined when $x = 6$. Therefore, the only solution is $x = -6$.